Understanding Rational Exponents and Solving Equations

The video tutorial covers the concept of rational exponents, explaining how they relate to radicals. It demonstrates solving equations involving fractional exponents, such as X to the one-half, three-halves, and two-fifths powers. The tutorial emphasizes isolating the power term, raising it to the reciprocal power, and verifying solutions.

What is a rational exponent?

• An exponent that is a fraction

• An exponent that is zero

• An exponent that is a whole number

• An exponent that is negative

How do you isolate the power term in an equation with rational exponents?

• By dividing both sides by the base

• By multiplying both sides by the reciprocal of the exponent

• By subtracting a constant from both sides

• By adding a constant to both sides

What is the reciprocal of the exponent 1/2?

• 1/2

• 2

• 1

• 1/4

In the equation 2x^(3/2) = 250, what is the first step to solve for x?

• Multiply both sides by 2

• Divide both sides by 2

• Add 1 to both sides

• Subtract 1 from both sides

What does raising a number to the two-thirds power involve?

• Taking the cube root and then squaring

• Cubing and then taking the square root

• Taking the square root and then cubing

• Squaring and then taking the cube root

How do you verify a solution to an equation with rational exponents?

• By graphing the equation

• By solving a different equation

• By checking if the original equation holds true

• By using a calculator

What is the fifth root of 1024?

• 16

• 8

• 4

• 2

In the equation (x-1)^(2/5) = 16, what is the next step after raising both sides to the 5/2 power?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 1 from both sides

• Add 1 to both sides

What is the solution to the quadratic equation x^2 - x - 2 = 0?

• x = -2 and x = 1

• x = 2 and x = -1

• x = 2 and x = 1

• x = 1 and x = -2

Why is it important to check solutions when dealing with square roots in equations?

• To find additional solutions

• To verify the solution satisfies the original equation

• To simplify the equation further

• To ensure the solution is positive